SMALL DOUBLING IN ORDERED GROUPS

DOI10.1017/S1446788714000019zbMath1301.20032MaRDI QIDQ5495478

Marcel Herzog, Gregory A. Freiman, Patrizia Longobardi, Mercede Maj

Publication date: 4 August 2014

Published in: Journal of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

nilpotent groupsordered groupsAbelian subgroupscombinatorial conditions on subsetsfinite subsetssmall doubling

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Subgroup theorems; subgroup growth (20E07) Nilpotent groups (20F18) Other combinatorial number theory (11B75) Ordered groups (06F15) Ordered groups (group-theoretic aspects) (20F60) Inverse problems of additive number theory, including sumsets (11P70) Arithmetic combinatorics; higher degree uniformity (11B30)

Related Items

Small doubling in ordered nilpotent groups of class 2 ⋮ On the structure of subsets of an orderable group with some small doubling properties ⋮ Direct and inverse problems in additive number theory and in non-abelian group theory ⋮ THE THEOREM FOR ORDERED GROUPS ⋮ A small doubling structure theorem in a Baumslag-Solitar group ⋮ On the probability of being a deficient square group on 2-element subsets ⋮ Small doubling in $m$-Engel groups ⋮ Groups with numerical restrictions on minimal generating sets ⋮ Unnamed Item ⋮ Sums of Dilates in Ordered Groups ⋮ Small doubling in ordered semigroups.

Cites Work

• Unnamed Item
• On subsets with small product in torsion-free groups
• Generalized arithmetical progressions and sumsets
• A polynomial bound in Freiman's theorem.
• Product set estimates for non-commutative groups
• On linearly ordered groups
• A Note on Freĭman's Theorem in Vector Spaces
• Freiman's Theorem in Finite Fields via Extremal Set Theory
• Freiman's theorem in an arbitrary abelian group
• On Ordered Groups

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